The basic functioning of a gamma camera is to "image" the distribution of radioactivity impinging on a detector. This may be used to estimate the distribution of sources emitting the radioactivity. The imaging consists of collecting the histogram, as a function of position, of the locations of where successive radioactive particles strike the detector.
A simplified gamma camera configuration consists of a scintillation detector, such as of sodium iodide, which converts radioactivity into visible light, and a group of photosensitive detectors, such as photomultipliers, which convert the visible light into electrical signals. The process of imaging is one where, for each scintillation event, the most likely position of scintillation is determined from the distribution of light detected by the array of photodetectors. It should be noted that the resolution of position is not limited to the size of the photodetectors. In other words, an algorithmic combination of photodetector signals is used to determine scintillation position with accuracies finer than the discrete sizes of the photodetectors.
A common algorithm for determining the event location from the distribution of photodetector signals is the centroid equation. Its one-dimensional form for the position &lt;x&gt; of a scintillation event is: &lt;x&gt;=.SIGMA.(qi*xi)/.SIGMA.qi, where qi is the signal on the i.sup.th photodetector, which is located at position x.sub.i, and the sum runs over all detectors.
The centroid equation has problems which limit its accuracy. Some of these problems are theoretical, namely non-linearity and noise.
With respect to non-linearity, the position determination &lt;x&gt; is not exactly equal to the correct position of the scintillation event. The error in &lt;x&gt; can be measured, however, and linearity correction look-up tables can be employed to improve its accuracy.
With respect to poor noise performance, photodetectors far from the scintillation event have little signal, but these small signals, with their inevitable noise, are added into the centroid equation with large coefficients, which essentially amplifies their noise contribution. This can be addressed by limiting the number of terms calculated for each scintillation event.
Some are due to practical implementation (energy and spatial dependence): in a standard, state-of-the-art gamma camera, the centroid algorithm is implemented using analog electronics. One of the theoretical disadvantages of the equation is its noise performance. It is for this reason that the standard analog implementation differs from the theoretical centroid equation. To reduce the effect of noise from distant photodetectors, the equation is currently implemented with a cutoff parameter. What this means is that only photodetectors having a signal greater than a predefined threshold are allowed to contribute to the centroid equation. If this cutoff is implemented as a simple number, i.e. includes all signals greater than 1.2 volts, then another problem arises with the equation: its position determination is not energy-independent. Thus the linearity correction tables will not be valid for all energies.
For example, if the energy of the radiation is doubled, then the distribution of signals qi will become qi.fwdarw.&gt;2*qi, and the resultant &lt;x&gt; will be different, as more qi will now be larger than the cutoff. If the cutoff used is a ratio, normalized to the total energy, then this problem is eliminated, but this is difficult to implement in analog electronics.
Another problem with the analog solution is the intermingling of several equations at the same location, and the subsequent linearity calibration. Successive events at the same location on the detector will not always give the same signals in the photodetectors. They will vary statistically as Poisson variables. This means that different events at the same detector location will have their locations determined using the centroid equation with a different number of terms. The linearity correction term measured for events at this location will be the algebraic average of the errors resulting from the position determination using several algorithms. This is a less accurate correction method than correcting each specific algorithm individually. A further understanding can be obtained from U.S. Pat. Nos. 4,095,107, 4,228,515, 4,584,478, 4,593,198, 4,782,233, 4,831,261, 4,837,439, and 4,859,852, which are incorporated herein by reference.